Now we consider the dwarf galaxy problem. For the central region of a typical dwarf galaxy according to Ref. [1]} we should have \(\rho _{DM} \sim 0.1 M_{\odot }\) /pc\(^{3}\)  and \(v\sim 50\)  km/s [2]}. If we convert this constraint to units of g/m\(^{3}\)  and compare this number with the mass density obtained in equation  (REF ) for our ALIP model, we find the required \(\rho _{DM}\sim 6.73\times 10^{-18}\)  g/m\(^{3}\)  is six orders of magnitude larger than the number obtained in equation  (REF ). Thus, this model cannot explain the missing satellite problem.
